A store sells two types of tables: plain and deluxe. When an orderfor a table ar
ID: 2913472 • Letter: A
Question
A store sells two types of tables: plain and deluxe. When an orderfor a table arrives, there is a 80% chance that the plain tablewill be desired.a) Out of five orders, what is the probability that no deluxetables will be desired?
b) Assume that each day five orders arrive and that today (Monday)an order came for a deluxe table. What is the probability that thefirst day in which one or more deluxe tables are again ordered willbe in three more days (Thursday)? What is the expected number ofdays until a deluxe table is desired?
c) Actually, the number of orders each day is a Poisson randomvariable with a mean of 5. What is the probability that exactlyfive orders will arrive on a given day?
Explanation / Answer
A store sells twotypes of tables: plain and deluxe. When an order for a tablearrives, there is a 80% chance that the plain table will bedesired. a) Out of five orders, what is the probability that no deluxetables will be desired?Prob{NO DeluxeOrdered} = Prob{ALL 5 Plain} = (0.80)^5 = 0.3277 b) Assume that each day five orders arrive and that today (Monday)an order came for a deluxe table. What is the probability that thefirst day in which one or more deluxe tables are again ordered willbe in three more days (Thursday)? What is the expected number ofdays until a deluxe table isdesired? Prob{NO Deluxe Ordered} = (0.80)^5 = 0.3277 Prob{At Least 1 Deluxe Ordered} = 1.0 - Prob{NO Deluxe} = 1.0 - (0.3277) = 0.6723 Prob{3 Days Until Next DeluxeOrdered} = {(0.3277)^2}*(0.6723) = 0.07219 c) Actually, the number of orders each day is a Poisson randomvariable with a mean of 5. What is the probability that exactlyfive orders will arrive on a givenday?Prob{Exactly 5 Orders} = (^k)*Exp[-]/(k!) = ((5)^(5))*Exp[-(5)]/(5!) = 0.1755 .
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